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Summary

Make math a snap with ALGEBRA FOR COLLEGE STUDENTS. Using everyday language and lots of examples, Kaufman and Schwitters show you how to apply algebra concepts and ace the test. This volume also comes with Interactive Skillbuilder CD-ROM. This program is packed with over 8 hours of video instruction to help it all make sense. Plus, you'll get the powerful web-based iLrn Homework program that makes your assignments a breeze. Get the grade you need with ALGEBRA FOR COLLEGE STUDENTS.

Table of Contents

Basic Concepts and Properties

1

(43)

Sets, Real Numbers, and Numerical Expressions

2

(9)

Operations with Real Numbers

11

(11)

Properties of Real Numbers and the Use of Exponents

22

(8)

Algebraic Expressions

30

(14)

Chapter 1 Summary

40

(1)

Chapter 1 Review Problem Set

41

(2)

Chapter 1 Test

43

(1)

Equations, Inequalities, and Problem Solving

44

(64)

Solving First-Degree Equations

45

(8)

Equations Involving Fractional Forms

53

(8)

Equations Involving Decimals and Problem Solving

61

(8)

Formulas

69

(11)

Inequalities

80

(7)

More on Inequalities and Problem Solving

87

(9)

Equations and Inequalities Involving Absolute Value

96

(12)

Chapter 2 Summary

103

(1)

Chapter 2 Review Problem Set

104

(3)

Chapter 2 Test

107

(1)

Polynomials

108

(57)

Polynomials: Sums and Differences

109

(6)

Products and Quotients of Monomials

115

(7)

Multiplying Polynomials

122

(7)

Factoring: Use of the Distributive Property

129

(8)

Factoring: Difference of Two Squares and Sum or Difference of Two Cubes

137

(6)

Factoring Trinomials

143

(8)

Equations and Problem Solving

151

(14)

Chapter 3 Summary

159

(1)

Chapter 3 Review Problem Set

160

(2)

Chapter 3 Test

162

(1)

Cumulative Review Problem Set (Chapters 1--3)

163

(2)

Rational Expressions

165

(59)

Simplifying Rational Expressions

166

(6)

Multiplying and Dividing Rational Expressions

172

(5)

Adding and Subtracting Rational Expressions

177

(8)

More on Rational Expressions and Complex Fractions

185

(10)

Dividing Polynomials

195

(6)

Fractional Equations

201

(8)

More Fractional Equations and Applications

209

(15)

Chapter 4 Summary

220

(1)

Chapter 4 Review Problem Set

221

(2)

Chapter 4 Test

223

(1)

Exponents and Radicals

224

(54)

Using Integers as Exponents

225

(7)

Roots and Radicals

232

(12)

Combining Radicals and Simplifying Radicals That Contain Variables

244

(6)

Products and Quotients Involving Radicals

250

(6)

Equations Involving Radicals

256

(5)

Merging Exponents and Roots

261

(7)

Scientific Notation

268

(10)

Chapter 5 Summary

274

(1)

Chapter 5 Review Problem Set

275

(2)

Chapter 5 Test

277

(1)

Quadratic Equations and Inequalities

278

(55)

Complex Numbers

279

(8)

Quadratic Equations

287

(8)

Completing the Square

295

(5)

Quadratic Formula

300

(8)

More Quadratic Equations and Applications

308

(12)

Quadratic and Other Nonlinear Inequalities

320

(13)

Chapter 6 Summary

327

(1)

Chapter 6 Review Problem Set

328

(2)

Chapter 6 Test

330

(1)

Cumulative Review Problem Set (Chapters 1--6)

331

(2)

Linear Equations and Inequalities in Two Variables

333

(58)

Rectangular Coordinate System and Linear Equations

334

(15)

Graphing Nonlinear Equations

349

(8)

Linear Inequalities in Two Variables

357

(5)

Distance and Slope

362

(12)

Determining the Equation of a Line

374

(17)

Chapter 7 Summary

387

(1)

Chapter 7 Review Problem Set

388

(2)

Chapter 7 Test

390

(1)

Functions

391

(72)

Concept of a Function

392

(10)

Linear Functions and Applications

402

(8)

Quadratic Functions

410

(11)

More Quadratic Functions and Applications

421

(10)

Transformations of Some Basic Curves

431

(11)

Combining Functions

442

(8)

Direct and Inverse Variation

450

(13)

Chapter 8 Summary

459

(1)

Chapter 8 Review Problem Set

460

(2)

Chapter 8 Test

462

(1)

Polynomial and Rational Functions

463

(57)

Synthetic Division

464

(5)

Remainder and Factor Theorems

469

(5)

Polynomial Equations

474

(12)

Graphing Polynomial Functions

486

(11)

Graphing Rational Functions

497

(11)

More on Graphing Rational Functions

508

(12)

Chapter 9 Summary

517

(1)

Chapter 9 Review Problem Set

518

(1)

Chapter 9 Test

519

(1)

Exponential and Logarithmic Functions

520

(69)

Exponents and Exponential Functions

521

(8)

Applications of Exponential Functions

529

(12)

Inverse Functions

541

(11)

Logarithms

552

(10)

Logarithmic Functions

562

(8)

Exponential Equations, Logarithmic Equations, and Problem Solving

570

(19)

Chapter 10 Summary

580

(1)

Chapter 10 Review Problem Set

581

(3)

Chapter 10 Test

584

(1)

Cumulative Review Problem Set (Chapters 1--10)

585

(4)

Systems of Equations

589

(59)

Systems of Two Linear Equations in Two Variables

590

(12)

Systems of Three Linear Equations in Three Variables

602

(7)

Matrix Approach to Solving Linear Systems

609

(11)

Determinants

620

(10)

Cramer's Rule

630

(7)

Partial Fractions (optional)

637

(11)

Chapter 11 Summary

643

(1)

Chapter 11 Review Problem Set

644

(2)

Chapter 11 Test

646

(2)

Algebra of Matrices

648

(38)

Algebra of 2 x 2 Matrices

649

(6)

Multiplicative Inverses

655

(7)

m x n Matrices

662

(9)

Systems of Linear Inequalities: Linear Programming

671

(15)

Chapter 12 Summary

682

(1)

Chapter 12 Review Problem Set

683

(2)

Chapter 12 Test

685

(1)

Conic Sections

686

(48)

Circles

687

(8)

Parabolas

695

(9)

Ellipses

704

(9)

Hyperbolas

713

(11)

Systems Involving Nonlinear Equations

724

(10)

Chapter 13 Summary

731

(1)

Chapter 13 Review Problem Set

732

(1)

Chapter 13 Test

733

(1)

Sequences and Mathematical Induction

734

(34)

Arithmetic Sequences

735

(8)

Geometric Sequences

743

(9)

Another Look at Problem Solving

752

(6)

Mathematical Induction

758

(10)

Chapter 14 Summary

764

(1)

Chapter 14 Review Problem Set

765

(2)

Chapter 14 Test

767

(1)

Counting Techniques, Probability, and the Binomial Theorem

768

(51)

Fundamental Principle of Counting

769

(6)

Permutations and Combinations

775

(9)

Probability

784

(6)

Some Properties of Probability: Expected Values

790

(11)

Conditional Probability: Dependent and Independent Events

801

(9)

Binomial Theorem

810

(9)

Chapter 15 Summary

815

(1)

Chapter 15 Review Problem Set

816

(2)

Chapter 15 Test

818

(1)

Appendix A: Prime Numbers and Operations with Fractions

819

(12)

Answers to Odd-Numbered Problems and All Chapter Review, Chapter Test, Cumulative Review, and Appendix A Problems